F.INV.RT in Google Sheets: Upper-Tail F Cutoffs
Use F.INV.RT in Google Sheets to convert upper-tail probabilities into F cutoffs, preserve FINV compatibility and allocate two-sided tail areas correctly.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =F.INV.RT(0.05,2,2) has expected result 19. It finds the F value with 5% of the distribution above it for numerator and denominator degrees of freedom both equal to 2.
Syntax and the right-tail probability
=F.INV.RT(probability, degrees_freedom1, degrees_freedom2)
All three arguments are required. There are no optional defaults. Google’s F.INV.RT reference requires a probability strictly between 0 and 1, numeric arguments and degrees of freedom at least 1. Fractional degrees of freedom are truncated to integers.
The function is explicitly synonymous with FINV in Google’s documentation. Its probability belongs to the right tail, rather than the cumulative area below the cutoff.
Worked example: upper-tail threshold table
Enter 0.5, 0.25, 0.1, 0.05 in A2:A5. Put 2 in D1 and 2 in E1. In B2, enter and fill down:
=F.INV.RT(A2,$D$1,$E$1)
| Right-tail probability | Expected F cutoff |
|---|---|
| 0.5 | 1 |
| 0.25 | 3 |
| 0.1 | 9 |
| 0.05 | 19 |
Smaller right-tail probabilities require larger cutoffs. This direction is a useful sanity check. Entering 5 rather than 5% or 0.05 does not represent a 5% tail and violates the documented probability domain.
For this special (2,2) distribution, the right tail is 1/(1+x), so the inverse is 1/probability-1. Thus =1/0.05-1 independently gives 19. The simplification follows from NIST’s general F-distribution definition and is not a universal formula for all degrees of freedom.
Check with the forward tail function
For the 5% cutoff:
=F.DIST.RT(19,2,2)
Expected result: 0.05. Google’s F.DIST.RT reference supplies the forward right-tail contract.
The equivalent left-tail inverse is:
=F.INV(1-0.05,2,2)
Expected result: 19. Google’s F.INV reference uses left-tail probabilities. The complement converts the question; replacing the name alone would change it.
Advanced application: one-sided and two-sided thresholds
For an ordered variance-ratio model with numerator degrees of freedom 6 and denominator degrees of freedom 8, the upper 5% cutoff is:
=F.INV.RT(0.05,6,8)
Expected result: 3.5805803198. A statistic of 3 is below that cutoff; a statistic of 4 is above it. These comparisons are arithmetic consequences of the chosen model and level, not automatic decisions about a real process.
If a two-sided 5% comparison is intended, the upper tail gets 2.5%, not the full 5%:
=F.INV.RT(0.025,6,8)
Expected upper cutoff: 4.6516955373. The lower counterpart can be obtained with =F.INV.RT(0.975,6,8), expected 0.1785834509. The two endpoint probabilities differ because this function always describes the area above the cutoff.
NIST’s variance-test reference distinguishes one-sided and two-sided alternatives. Choose the alternative before using the observed data to decide which tail looks more favorable.
Degrees of freedom are ordered parameters
For the usual ratio of two sample variances, a sample size of 7 in the numerator and 9 in the denominator gives degrees of freedom 6 and 8. Reverse the statistic and the degree-of-freedom roles must reverse with it.
For example, =F.INV.RT(0.05,8,6) gives 4.1468041623, rather than 3.5805803198. The parameters are not interchangeable merely because both are counts.
The inverse page’s at-least-1 restriction differs from the greater-than-1 wording on the forward distribution pages. These guides preserve each documented contract and use values above 1 for forward checks, without claiming native resolution of that boundary difference.
Errors and troubleshooting
Verify the probability scale, tail direction, parameter order and numeric types. Keep full precision for round-trip checks. A rounded cutoff can produce a tail area slightly different from the original probability.
The reviewed reference does not establish a complete native error-token, blank or text coercion matrix, or accuracy arbitrarily near probability endpoints. Those gaps are not filled from another spreadsheet engine. The function’s output also does not establish that the data meet the assumptions for an exact variance-ratio test.
Availability and verification
Google explicitly documents FINV as the same right-tail inverse function. Original introduction date, first supported version and last functioning numbered release were not established for the rolling Sheets service.
NOT_TESTED_IN_GOOGLE_SHEETS. Individual Google pages and NIST mathematical references were inspected on October 17, 2026. Quantiles, complements and forward tails were independently calculated; no native session or screenshot is claimed.